Exemplary embodiments of the present invention are directed to a method for determining the geographic coordinates of pixels in SAR images.
Using SAR image to determine the position of a target at great distances (20 km-100 km) is frequently imprecise due to the errors in the SAR images. The errors in the SAR images typically result from azimuth errors and distortion effects. (foreshortening, layover).
U.S. Pat. No. 5,659,318 A discloses an interferometric method in which images of a target region generated using two spatially separated SAR antennas are analyzed in terms of their phase difference, and the recording position of the SAR images is known.
The known approach to coordinate determination of a target from an SAR image will be explained first:
The basis for this is what is called a WGS84 ellipsoid. The World Geodetic System 1984 (WGS 84) is a geodetic reference system forming the uniform foundation for positional information on the earth or near-earth space. It is composed of                a simple three-dimensional reference surface, the reference ellipsoid that is roughly matched to the surface of the earth;        a more detailed model for the shape of the earth that deviates from this idealized shape, the so-called geoid;        twelve fundamental stations distributed across the earth, through which the relationship between these models and the earth's crust is defined by providing (time-dependent) coordinates (the so-called reference frame).        
The system is the geodetic foundation of the Global Positioning Systems (GPS) that enables appropriate satellites (NAVSTAR satellites) to survey the earth and provide orientation.
The key parameters in an SAR are defined in FIGS. 1a and 1b. A typical SAR configuration is illustrated in FIG. 1a. The sensor platform, e.g., an aircraft, is moving at altitude h above the ground at velocity v along the X axis. The radar illuminates sideways a region on the ground. The optimum viewing direction for an SAR is 90° relative to the direction of velocity vector v. Viewing directions that deviate from the optimum viewing direction negatively affect the resolution and the cost/complexity of SAR image generation. The size of the radar antenna corresponds to the real aperture. This size is kept relatively small to allow the radar antenna to be carried on the sensor platform. However, the size of the antenna, or the aperture, determines the resolution. The larger the antenna, the better the resolution. In order to achieve high resolution despite the small antenna, a large antenna is generated artificially. This occurs by having the sensor platform fly along the aperture of an imaginary large antenna and collecting the reflected radar pulses at each section of the imaginary large antenna. The sensor platform must in other words fly the length of a synthetic aperture in order to collect the data for an SAR image.
The key SAR parameters are illustrated more precisely in FIG. 1b. The term S denotes the position of the sensor platform, while the vector v denotes the associated velocity. The coordinate system is chosen so that v points along positive axis X. Point T is mapped to the center of the SAR image. The straight line LOS (line of sight) denotes the connecting line between position S of the sensor platform and point T. The length of straight-line LOS corresponds to the range gate R of the SAR. The projection of velocity vector onto straight line LOS yields the radial approach velocity vr of the sensor platform toward point T. The angle Ψ between velocity vector v and straight line LOS is designated here as the squint angle. Projection of straight line LOS onto a plane that runs through point S and is parallel to the XY plane produces the straight line HLOS (horizontal line of sight). The angle ϵ between LOS and HLOS is called the elevation angle.
In order to effect a typical determination of coordinates for a target from an SAR image, the coordinate of the center of the SAR image is determined first. The coordinate of a pixel on the SAR image that has been recognized as the target is then computed. The SAR parameters introduced above are used to determine the coordinates of the image center.
The relevant parameters for the typical coordinate determination of a target from an SAR image are illustrated in FIG. 2a. Sensor platform S is located at altitude H above the WGS84 ellipsoid, which is represented here in a highly enlarged manner as a plane. Together with the squint angle Ψ and the distance R (range gate) to the image center, velocity vector v defines a cone. This cone determines the SAR configuration. The base of the cone defines a circle of radius r=R sin(Ψ). The geographic coordinate of the SAR image center is located at the intersection between this circle and the surface of the earth. There are two points on the graph where the circle intersects the surface of the earth. Since, however, it is known in which direction the SAR sensor is looking, one intersection point can obviously be excluded.
Once the geographic coordinate P0 of the SAR image center has been computed, the geographic coordinate of a pixel recognized as the target can be calculated on the SAR image. FIG. 2b outlines the key parameters here. To this end, the local tangential vectors nr and ncr normalized to one on the WGS84 ellipsoid are calculated at point P0. Since the pixel coordinates px and py are known relative to the SAR image center, the known resolutions δx and δy can be used to calculate the displacement vector d from point P0 to the point that corresponds to the pixel, as follows:{right arrow over (d)}=δxpx{right arrow over (ncr)}+δypy{right arrow over (nr)}
Simple vector addition can then be used to calculate the geographic coordinate of the target pixel from the geographic coordinates of image center P0 and displacement vector d. Calculation of the geographic coordinates of the point that corresponds to the pixel is prior-art knowledge and is familiar to a person skilled in the art.
In the determination of coordinates for a target from an SAR image using the approach familiar from prior art, the above-described cone contributes to determining the coordinates of the target. However, the position of this cone in space is determined relative to the velocity vector. If this velocity vector is not known precisely, then an error results in the coordinate determination. In typical SAR systems, this error can amount to up to 100 meters in the azimuth direction, the direction of the velocity vector. In addition, the assumption is made based on the determination of the geographic coordinates of the image center that the target plane is flat. However, SAR produces typical effects such as foreshortening or layover, a displacement of the pixel corresponding to the target point, and this results in an additional error in the calculation of the displacement vector to the target.
Exemplary embodiments of the present invention provide a method by which the error in the position determination can be reduced.
According to the invention, the coordinates of the corresponding pixels in the SAR images and the corresponding range gates are used to determine in each case the distance between a corresponding resolution cell on the ground and the respective recording position of the respective SAR image, and the determined distances and associated recording positions for the SAR images are used to determine the geographic coordinates of the corresponding pixels in the SAR images by employing an WGS84 ellipsoid.